A high order linear model for the prediction of internal lee waves at the main sill of the Strait of Gibraltar

A linear theory for the physical fields in the water column under the action of large amplitude internal lee waves at the main sill of the Strait of Gibraltar is developed. The procedure is a combination of the perturbation and normal modes methods in order to study steady resonant conditions. The lowest order linear approach of the methodology resumes the Taylor-Goldstein equation, which can reconstruct the main features of the observed fields but the high order approach gives the finest structure and sometimes the largest contributions. The role of the non-linear terms is investigated up to the second order taking into account the non-linear interactions between modes, leading to an effective reconstruction of the whole water column for the velocity field.